A family of well-known orthonormal functions, the set of
Hermite functions, is proposed as a suitable basis for expanding the
Stokes profiles of any spectral line. An expansion series thus
provides different degrees of approximation to the Stokes spectrum,
depending on the number of basis elements used (or on the number of
coefficients). Hence, an usually large number of wavelength samples,
may be substituted by a few such coefficients, thus reducing
considerably the size of data files and the analysis of observable
information. Moreover, since the set of Hermite functions is an
universal basis, it promises to help in modern inversion techniques
of the radiative transfer equation that infer the solar physical
quantities from previously compiled look-up tables or artificial
neural networks. These features appear to be particularly important
in modern solar applications producing huge amounts of
spectropolarimetric data and on near-future, on-line
applications aboard spacecrafts.

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